Simulation of Simplicity for Geometric Objects in Projective Space

摘要

Simulation of Simplicity (SOS) is a method for removing special cases from geometric computation and detection algorithms. Although SOS has been proposed and used in the field of computational geometry, there has been limited application in the field of computer aided design and solid modeling. Homogeneous coordinates has become a standard tool in conducting geometric computations. Homogeneous coordinates are currently applied to conduct geometric computations not only to sets in Euclidean space, but in Projective space as well. The consistent use of homogeneous coordinates also makes major contributions in the elimination of special cases in geometric computations. A theory of geometric computations become by combining the SOS theory with the consistent use of homogeneous coordinates. This paper proposes a method of using homogeneous coordinates to conduct geometric computations of projective primitives based on the SOS method. Applications to geometric algorithms such as point-in-polygon tests, point-in-polyhedron tests are shown.